To complete the square for the quadratic function f(x) = x^2 - 2x - 8, we can follow these steps:
1. Group the x^2 and x terms together:
f(x) = (x^2 - 2x) - 8
2. Take half of the coefficient of the x term, square it, and add it inside the parentheses:
f(x) = (x^2 - 2x + 1 - 1) - 8
f(x) = (x^2 - 2x + 1) - 9
3. Simplify the expression inside the parentheses:
f(x) = (x - 1)^2 - 9
Therefore, the function f(x) can be written in vertex form as f(x) = (x - 1)^2 - 9.